Exxon Chief Executive

Darren Woods

was also re-elected to the board along with seven of Exxon’s candidates, while the vote was too close to call for five nominees, the company said.

The vote culminated one of the most expensive proxy fights ever. It was an enormous blow to Mr. Woods, who personally campaigned against Engine No. 1.

“We welcome all of our new directors and look forward to working with them constructively,” Mr. Woods said in a statement.

Engine No. 1 sought four seats on Exxon’s board and argued the Texas oil giant should commit to carbon neutrality, effectively bringing its emissions to zero—both from the company and its products—by 2050, as some peers have.

It nominated four directors—

Gregory Goff,

Kaisa Hietala,

Alexander Karsner

and

Anders Runevad

—and Mr. Goff and Ms. Hietala were elected Wednesday, according to the preliminary tally. Mr. Goff is the former chief executive of Andeavor, which was one the largest U.S. refiners before being purchased for more than $20 billion by

Marathon Petroleum Corp.

MPC 1.32%

in 2018, while Ms. Hietala is a former executive vice president of renewable products at Finnish refiner

Neste Oyj.

Engine No. 1 accused Exxon’s board of presiding over the company’s demise and argued its own candidates had the qualifications to help Exxon better navigate the energy transition.

The hedge fund called for Exxon to gradually diversify its investments to be ready for a world that will need fewer fossil fuels in coming decades. Exxon defended its strategy to expand drilling, saying demand for fuels and plastics will remain strong for years to come, and pointed to a new carbon capture and storage business unit as evidence it is taking climate change seriously.

Peter Bryant,

a managing partner at business consultant Clareo, said Exxon was vulnerable because it hasn’t provided a good return from fossil fuels for years and doesn’t get credit from sustainability-focused investors because it hasn’t invested in renewable energy.

“It’s the worst of both worlds,” Mr. Bryant said.

Andrew Logan,

senior director for oil and gas at Ceres, a nonprofit focused on sustainability that supported Engine No. 1’s campaign, said it would be difficult for Mr. Woods to retain his position as CEO after the vote.

“That certainly calls his leadership into question,” Mr. Logan said. “There is no going back to the Exxon of old nor should there be.”

Exxon and Mr. Woods had made a series of changes, long sought by some investors, since the campaign began, including creating a business unit for carbon emissions-reducing technologies and disclosing for the first time the emissions from Exxon products.

But Engine No. 1 said those moves were inadequate. Despite a series of calls and meetings, the two sides were unable to agree to a common set of directors. The fund said Exxon had proposed a deal of sorts, offering Engine No. 1 in January a chance to rubber-stamp and take credit for three candidates Exxon later appointed to the board. Engine No. 1 said it refused.

Exxon said it reviewed Engine No. 1’s candidates and determined they didn’t meet the board’s standards. In an interview last week, Exxon lead director

Kenneth Frazier

said Exxon had asked the fund to sign a nondisclosure agreement that would have allowed it to review board candidates Exxon ultimately proposed, but the fund declined.

Exxon and Engine No. 1 spent much of their time courting institutional investors. But the company has more than two million shareholders, many of them individual investors, and they played a key role in the outcome.

Elizabeth Wilder has owned Exxon stock her entire life after inheriting it from her grandfather, a former Exxon employee. Ms. Wilder, a self-described homemaker in Houston, said she previously always backed management’s board nominees. This time, she voted for three of Engine No. 1’s candidates.

“Exxon has failed spectacularly by every available measure: stock value, relative diminishment of value compared to peers, capital allocation, environmental stewardship reporting,” Ms. Wilder said. “The people who oversaw the past decade of wealth destruction should be held accountable.”

Write to Christopher M. Matthews at christopher.matthews@wsj.com